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An ideal gas expands from state (P(1), V...

An ideal gas expands from state `(P_(1), V_(1))` to state `(P_(2), V_(2))`, where `P_(2) = 2P_(1)` and `V_(2) = 2V_(1)`. The path of the gas is expressed by the following relation,
`P = P_(1) [1 + ((V - V_(1))/(V_(1)))^(2)]`

A

`P_(1) V_(1)`

B

`4//3 P_(1) V_(1)`

C

`2P_(1) V_(1)`

D

`4P_(1) V_(1)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • An ideal gas is transformed from state A (P_(1), V_(1)) to the state B (P_(2), V_(2)) through path AB. In this process the work done by the gas is

    A
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    B
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    C
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    D
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  • An ideal gas is expanded from (P_(1), V_(1), T_(1)) to (P_(2), V_(2), T_(2)) under different conditions. The correct statement(s) among the following is (are)

    A
    The work done by the gas is less when it is expanded reversibly from `V_(1)` to `V_(2)` under adiabatic conditions as compared to that when expanded reversibly from `V_(1)` to `V_(2)` under isothermal conditions
    B
    The change in internal energy of the gas is (i) zero, if it is expanded reversibly with `T_(1)=T_(2)`, and (ii) positive, if it is expanded reversibly under adiabatic conditions with `T_(1) ne T_(2)`
    C
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    D
    The work done on the gas is maximum when it is compressed irreversibly from `(P_(2), V_(2))` to `(P_(1), V_(1))` against constant pressure `P_(1)`

  • A gaseous system changes from state A (P_(1), V_(1),T_(1)) to B (P_(2), V_(2),T_(2)) to C(P_(3), V_(3),T_(3)) and finally from C to A . The whole process may be called :

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    Reversible process
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    Cyclic process
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    D
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